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gnits

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- Homework Statement
- To find the modulus of elasticity of a light elastic string

- Relevant Equations
- Moments

Could I please ask for help with the following question?

Four uniform rods of equal length l and weight w are freely jointed to form a framework ABCD. The joints A and C are connected by a light elastic string of natural length a. The framework is freely suspended from A and takes up the shape of a square. Find the modulus of elasticity of the string.

Formula for modulus of elasticity is M = T * a/x where T is the tension in the string, a the natural length and x the extension.

Here's my diagram:

The book answer is M = 2aw / ( sqrt(2) * l - a)

I have shown from the diagram above that the extension of the string is sqrt(2) * l - a

So what remains is for me to show that the tension in the string is 2w.

I've split the diagram in half and shown the internal reactions in the hinges at B and D and by considering section BC alone and taking moments about C have shown that Y = w/2

But I'm not seeing a way to find T = 2W. I suspect my force labelling may be wrong?

Thanks,

Mitch.

Four uniform rods of equal length l and weight w are freely jointed to form a framework ABCD. The joints A and C are connected by a light elastic string of natural length a. The framework is freely suspended from A and takes up the shape of a square. Find the modulus of elasticity of the string.

Formula for modulus of elasticity is M = T * a/x where T is the tension in the string, a the natural length and x the extension.

Here's my diagram:

The book answer is M = 2aw / ( sqrt(2) * l - a)

I have shown from the diagram above that the extension of the string is sqrt(2) * l - a

So what remains is for me to show that the tension in the string is 2w.

I've split the diagram in half and shown the internal reactions in the hinges at B and D and by considering section BC alone and taking moments about C have shown that Y = w/2

But I'm not seeing a way to find T = 2W. I suspect my force labelling may be wrong?

Thanks,

Mitch.

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